In today's technological society, high level mathematics is being taught to students at an earlier age than ever before. One such high level concept is that of numerical sequences. A numerical sequence is a sequence of numerical entities arranged in correspondence with naturally ordered whole numbers, i.e., 1,2,3, . . . The numerical entities are called "terms". Each term is generically identified by a term identifier such as "n". The term identifier is a variable which can be assigned a natural number to identify a particular term. For example, the terms of a particular numerical sequence are represented by "U.sub.n " where n is the term identifier.
Where n=3, U.sub.3 represents the third term of the numerical sequence U.sub.n. When n can equal only a finite number of values, the numerical sequence is finite. When n can equal an infinite number of values, the numerical sequence is infinite.
A typical task is to generate a solution for a particular term of a numerical sequence. The terms of a numerical sequence are traditionally solved using a user-programmed device such as a computer or calculator. One problem is that these devices are relatively expensive. A consequence of this expense is that few high school students have access to these devices.
A second problem with these user-programmed devices is that a program must be written to solve for the terms of the numerical sequence. Unfortunately, many students lack the necessary programming skills to write such a program. Most of a student's initial time and effort, therefore, is spent learning how to program the calculator. This expenditure of time and effort detracts from the student's learning of the concept of numerical sequences.
A third problem with many user-programmed devices is that they do not provide an adequate visual display. A term or group of terms can be represented in a variety of forms. Of these forms, the most useful for teaching include mathematical notation and graph. Existing programmable calculators do not translate the program code describing the terms into either a mathematical notation or graph form.
Therefore, a need has arisen for an improved calculator, accessible to a large number of students, for generating solutions to the terms of a numerical sequence.